# Full text of "Analytical Mechanics"

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```WORK                                       IS
3. Find the mechanical advantage of the jack-screw. Let p be the pitch of the screw, I the length of the lever arm, F the for applied and P the force derived.   Then since at any instant the system is supposed to be in equilibrium the virtual work, due      ^ to a small displacement, must vanish.  Let , dd denote a small angular displacement  l^ and dh the corresponding rise of the screw.      ^ **-.-.. Then if G denotes the torque applied the virtual work takes the form
But G = F • I and dh = ™- p.   Therefore
2i7T
FIG. 100.
Hence the mechanical advantage, which is the quotient of the force d rived to the force applied, is
P^2irl
F      p'
PROBLEMS.
1.   By the application of the principle of virtual work derive the e pression for the mechanical advantage of
(a)  the lever;       -—-^
(b)  the wheel and axle;
(c)  the hydraulic press;
(d)  the pulley (a) of problem 13 on page 21;
(e)  the pulley (b) of problem 13 on page 21;
(f)  the pulley (c) of problem 13 on page 21;
(g)  the pulley (d) of problem 13 on page 21.
2.   Apply the principle of virtual work to
(a)  illustrative problem 1 on page 17;
(b)  problem 4 on page 20;
(c)  problem 6 on page 46;
(d)  problem 16 on page 47.
3.   Four rods of equal weight W are freely jointed so as to form square.   The system is suspended vertically from one of the joints, string of negligible weight connects two of the joints so as to keep tl square shape of the system.   Find the tension of the string.```